zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Fractional order differential equations on an unbounded domain. (English) Zbl 1179.26015
Summary: We are concerned with the existence of bounded solutions of a boundary value problem on an unbounded domain for differential equations involving the Caputo fractional derivative. Our results are based on a fixed point theorem of Schauder combined with the diagonalization method.

26A33Fractional derivatives and integrals (real functions)
26A42Integrals of Riemann, Stieltjes and Lebesgue type (one real variable)
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
[1] Glockle, W. G.; Nonnenmacher, T. F.: A fractional calculus approach of self-similar protein dynamics, Biophys. J. 68, 46-53 (1995)
[2] Hilfer, R.: Applications of fractional calculus in physics, (2000) · Zbl 0998.26002
[3] Metzler, F.; Schick, W.; Kilian, H. G.; Nonnenmacher, T. F.: Relaxation in filled polymers: A fractional calculus approach, J. chem. Phys. 103, 7180-7186 (1995)
[4] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[5] Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. calc. Appl. anal. 5, 367-386 (2002) · Zbl 1042.26003
[6] Kilbas, A. A.; Srivastava, Hari M.; Trujillo, Juan J.: Theory and applications of fractional differential equations, North-holland mathematics studies 204 (2006) · Zbl 1092.45003
[7] Lakshmikantham, V.; Leela, S.; Vasundhara, J.: Theory of fractional dynamic systems, (2009) · Zbl 1188.37002
[8] R.P Agarwal, M. Benchohra, S. Hamani, A survey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math. (in press) · Zbl 1198.26004 · doi:10.1007/s10440-008-9356-6
[9] Ahmad, B.; Nieto, J. J.: Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Bound. value probl. 2009 (2009) · Zbl 1167.45003
[10] M. Belmekki, J.J. Nieto, R. Rodriguez-Lopez, Existence of periodic solution for a nonlinear fractional differential equation, Bound. Value Probl. (in press) Art. ID 324561 · Zbl 1181.34006 · doi:10.1155/2009/324561
[11] Benchohra, M.; Graef, J. R.; Hamani, S.: Existence results for boundary value problems of nonlinear fractional differential equations with integral conditions, Appl. anal. 87, No. 7, 851-863 (2008) · Zbl 1198.26008 · doi:10.1080/00036810802307579
[12] Benchohra, M.; Hamani, S.: Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative, Topol. methods nonlinear anal. 32, No. 1, 115-130 (2008) · Zbl 1180.26002
[13] Benchohra, M.; Hamani, S.; Ntouyas, S. K.: Boundary value problems for differential equations with fractional order, Surv. math. Appl. 3, 1-12 (2008) · Zbl 1157.26301 · http://www.utgjiu.ro/math/sma/v03/a01.html
[14] Chang, Y. -K.; Nieto, J. J.: Some new existence results for fractional differential inclusions with boundary conditions, Math. comput. Model. 49, 605-609 (2009) · Zbl 1165.34313 · doi:10.1016/j.mcm.2008.03.014
[15] Ouahab, A.: Some results for fractional boundary value problem of differential inclusions, Nonlinear anal. 69, No. 11, 3877-3896 (2008) · Zbl 1169.34006 · doi:10.1016/j.na.2007.10.021
[16] Belarbi, A.; Benchohra, M.; Ouahab, A.: Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces, Appl. anal. 85, 1459-1470 (2006) · Zbl 1175.34080 · doi:10.1080/00036810601066350
[17] Benchohra, M.; Henderson, J.; Ntouyas, S. K.; Ouahab, A.: Existence results for fractional order functional differential equations with infinite delay, J. math. Anal. appl. 338, No. 2, 1340-1350 (2008) · Zbl 1209.34096 · doi:10.1016/j.jmaa.2007.06.021
[18] Belarbi, A.; Benchohra, M.; Hamani, S.; Ntouyas, S. K.: Perturbed functional differential equations with fractional order, Commun. appl. Anal. 11, No. 3--4, 429-440 (2007) · Zbl 1148.34042
[19] Heymans, N.; Podlubny, I.: Physical interpretation of initial conditions for fractional differential equations with Riemann--Liouville fractional derivatives, Rheol. acta 45, No. 5, 765-772 (2006)
[20] R.P. Agarwal, M. Benchohra, S. Hamani, S. Pinelas, Boundary value problem for differential equations involving Riemann--Liouville fractional derivative on the half line, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. (in press) · Zbl 1208.26012 · http://dcdis001.watam.org/volumes/abstract_pdf/2011v18/v18n2a-pdf/7.pdf
[21] Granas, A.; Dugundji, J.: Fixed point theory, (2003) · Zbl 1025.47002
[22] Agarwal, R. P.; Regan, D. O’: Infinite interval problems for differential, difference and integral equations, (2001)
[23] Agarwal, R. P.; Regan, D. O’: Boundary value problems of nonsingular type on the semi-infinite interval, Tohoku. math. J. 51, 391-397 (1999) · Zbl 0942.34026 · doi:10.2748/tmj/1178224769